d. One should observe that either $x=0$ in every point of the trajectory, or in no point; and that $y=0$ in every point of the trajectory, or in no point. It allows us to make a "skeleton'' of the phase portrait (see attachment), impose local pictures on it and finally draw a global portrait

a. Some students missed some stationary points and/or reported wrong points. All further analysis in the wrong points was ignored as irrelevant. For all three correct points found I gave 10pts, with a reduction of 3 pts for each missed points, and 1pts for extra points (only for those who found 3 correct points).

b. Linearization was easy, but some borked it. Finding eigenvalues was supposed to be a breeze but ...One does not need to solve any equations to find eigenvalues of the diagonal or triangular matrices (some students wrote wrong equations and found wrong eigenvalues). Also eigenvectors of the diagonal matrices are obvious, and of the triangular are easy.

Not everyone found correctly eigenvalues of the matrix at $(2,3)$. T recall, that they are $1\pm i\sqrt{5}$. One does not need to look for eigenvectors, however one should look at the sign of bottom left element of the matrix and conclude what is the direction of rotation (I have not subtracted points for missing justification that it is counter-clockwise)

c. Drawing of the local pictures. At (0,0) mant=y draw incoming and outgoing lines like X instead of +, others indicated the wrong directions. Point $(-1,0)$ was more difficult. And in $(2,3)$ some draw "hairy monsters"

d. Even when all local pictures were drawn correctly, some students draw intersecting lines (trajectories do not intersect!) and not everyone observed that $x=0$ and $y=0$ consist of trajectories (see "skeleton" in my post above)

In some papers with no calculations or with calculations, leading to wrong conclusions) there are "miraculously" correct pictures. Those were discarded because "only solutions (not just answers) are evaluated".